Just last week, in the wake of the deadly Las Vegas mass shooting, Feinstein introduced a bill that would ban the sale, transfer, importation, manufacture or possession of bump stocks, trigger cranks and similar accessories that allow a semiautomatic rifle's rate of fire to mimic fully automatic fire. A dozen of these devices were found in the hotel room of the Las Vegas shooter. The measure has 26 Democratic co-sponsors.

The nation's largest gun lobby, the National Rifle Association, suggested in a statement that it would support regulations that would allow policymakers to ban bump stocks.

But Feinstein told CBS' "Face the Nation" that regulation alone will not enable policymakers to ban bump stock devices.

"We need a law. It can't be changed by another president," Feinstein told CBS' John Dickerson.

"Right now we are seeing one president changes actions of a president that came before him and that would happen in this area," she added. "So we need a law and we have an opportunity to get it. I hope Americans will step up and say enough is enough – Congress, do something."

The Democrat will be 85-years-old as she goes before voters next year, and would be 91 by the time her next term ends, if she's elected to a fifth full term.